## Mathematics Questions for Defence Exams : 24th May 2019 – English

Dear Students, DefencePrep is providing you all with Mathematics questions Quiz, Maths Quiz for Air Force Exam and other Defence Exams. The questions asked in Mathematics Section of most of the defence examinations are based on the topics from Mathematics of Class 11th and 12th.

The questions asked in this section are complex and comparatively difficult but once attempted with high accuracy, can fetch you full marks in this section.

Practice on a daily basis helps one dive into the core concepts of a subject and thus, help her perform to the best of her ability in the real examinations. So, attempt the daily quizzes being provided by DefencePrep and score to the maximum in Mathematics Section of all sorts of defence examinations.

**QUESTIONS**

**1. If $x$ is a variable of binomial distribution, whose mean is 3 and variance 2, then get the value of $p(x\ge 8)$**

a $\frac{19}{3}$

b. $ {\left(\frac{19}{3}\right)}^{9} $

c. $ \frac{19}{{\left(3\right)}^{9}} $

d. $ \frac{{\left (19\right)}^{9}} {3} $

**2. If the equation of two regression lines is $2x-9y+6=0$ and $x-2y+1=0$, then find correlation coefficient between $x$ and $y$.**

a 2/3

b. -2/3

c. 3/2

d. 1/2

**3. Karl Pearson’s correlation coefficient depends**

a Only on the change of the origin, not on the change of scale

b. Only on change of scale, not on change of origin

c. On the change of both the scales and the origin of the scales

d. Neither on the change of origin, nor on the change of scale

**4. If the correlation coefficient between two variables $ x $ and $ y $ is zero, then**

a There is no correlation between $ x $ and $ y $

b. Value of $ y $ decreases when value of $ x $ increases

c. Value of $ y $ increases when value of $ x $ increases

d. The variables can also be related to $ x $ and $ y $

**5. If the standard deviation of $ x $ is $ \sigma $, then the variable deviation of variable $ \mu = \frac {ax + b} {c} $, where $ a, b $ and $ c $ is constant, will be**

a $ \mu = \frac {ax + b} {c} $

b. $ \left | \frac {a} {c} \right | \sigma $

c. $ \left | \frac {b} {c} \right | \sigma $

d. $ \left | \frac {b} {c} \right | \sigma $

**6. Two incidents are $ A $ and $ B $ that are $ P \left (A \right) = \frac {1} {4}, P \left (\frac {B} {A} \right) = \frac {1} {2}, P \left (\frac {A} {B} \right) = \frac {1} {4} $, then which of the following statements is true?**

1. $ P \left (\frac {{A} ^ {C}} {B ^ {C}} \right) = \frac {3} {4} $

2. Events $ A $ and $ B $ are mutually exclusive

3. $ P \left (\frac {A} {B} \right) + P \left (\frac {A} {{B} ^ {2}} \right) = 1 $

a only 1

b. 1 and 2

c. 1 and 3

d. 2 and 3

**7. If $ A $ and $ B $ are two free events such that $ P \left (A \right)> 0 $ and $ P \left (B \right) \neq 1 $, then $ P \left ( Find the value of \overline {A} / \overline {B} \right)**

a $ 1-P (A / B) $

b. $ 1-P \left (\overline {A} / \overline {B} \right) $

c. $ \frac {1-P \left (A + B \right)} {P \left (\overline {B} \right)} $

d. $ P \left ({\overline {A}} \right) / P \left ({\overline {B}} \right) $

**8. The elevation angle is $ {30} ^ {o} $ from a point located 200 meters above a lake and the angle of reflection in its lake is ${ 60} ^ {o} $, if the cloud is high What is it distance ?**

a 200m

b. 300m

c. 400m

d. 600m

**9. Consider the following statements****1. Heterogeneous lines $ \frac {x + 3} {-4} = \frac {y-6} {3} = \frac {z} {2} $ and $ \frac {x + 2} {-4} = \frac {y} {1} = \frac {z-7} {1}$ is the minimum distance between****2. Two lines are horizontal lines, if there is no bottom through both****Which of the above statements is / are true**

a only 1

b. only 2

c. 1 and 2

d. None of these

**10. Find out the probability of not having a 53 Mondays in a leap year.**

a $ \frac {5} {7} $

b. $ \frac {7} {5} $

c. $ \frac {1} {5} $

d. $ \frac {1} {7} $

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